Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?

It is given in the question that,

90% of the people are right handed

Let p denotes the probability of people that are right handed and q denotes the probability of people that are left handed

∴

And,

Now, by using the binomial distribution probability of having more than 6 right handed people can be given as:

Hence, the probability of having more than 6 right handed people:

= 1 – P (More than 6 people are right handed)

=

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